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arXiv:2309.11034 · Results in Physics

Multipartite entanglement detection via generalized Wigner–Yanase skew information

Yan Hong, Yabin Xing, Limin Gao, Ting Gao, Fengli Yan

Published Mar 28, 2024• 3 citations
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Abstract

The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory.In this paper, we investigate $k$-nonseparability and $k$-partite entanglement of $N$-partitequantum systems from the perspective of the generalized Wigner-Yanase skew information introduced by Yang $et$ $al$.[\href{https://doi.org/10.1103/PhysRevA.106.052401}{Phys. Rev. A \textbf{106}, 052401 (2022)}]. More specifically, we develop two different approaches in form of inequalities to construct entanglement criteria, which are expressed in terms of the generalized Wigner-Yanase skew information.Any violation of these inequalities by a quantum state reveals its $k$-nonseparability or $k$-partite entanglement,so these inequalities present the hierarchic classifications of $k$-nonseparability or $k$-partite entanglement for all $N$-partite quantum states from $N$-nonseparability to $2$-nonseparability or from $2$-partite entanglement to $N$-partite entanglement, which are more refined than well-known ways. It is shown that our results reveal some $k$-nonseparability and $k$-partite entanglement that remain undetected by other methods,and these are illustrated through some examples.

DOI
10.1016/j.rinp.2024.107624

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Abstract Multipartite quantum entanglement, as a core quantum resource, is fundamental to the advancement of quantum science and technology. In multipartite quantum systems, there are two kinds of quantum entanglement: k -nonseparability and k -partite entanglement. In this paper, we propose sufficient criteria for detecting k -nonseparability and k -partite entanglement by using the generalized Wigner–Yanase skew information and mutually unbiased measurements. Examples are given to demonstrate the detection capability and advantages of these criteria. As an application, an example of recognizing the networks by detecting the depth of quantum networks is given.
Quantum entanglement plays a critical role in many quantum applications, but detecting entanglement, especially in multipartite or high-dimensional quantum systems, remains a challenge. In this paper, we propose several families of entanglement criteria for detecting entanglement in multipartite or high-dimensional quantum states by the generalized Wigner-Yanase skew information Is(ρ,X)I^s(ρ,X)Is(ρ,X) for −1≤s≤0-1\leq s\leq0−1≤s≤0 and variance. We also reveal a complementary character between the criteria based on the generalized Wigner-Yanase skew information and an alternative one based on variance through specific examples. We illustrate the merits of these criteria and show that the combination of the entanglement criteria has a stronger detection capability, as it is capable of detecting entangled states that remain unrecognized by other criteria.
Abstract Quantum entanglement plays a critical role in many quantum applications, but detecting entanglement, especially in multipartite or high-dimensional quantum systems, remains a challenge. In this paper, we propose several families of entanglement criteria for detecting entanglement in multipartite or high-dimensional quantum states by the generalized Wigner–Yanase skew information I s ( ρ , X ) for − 1 ⩽ s ⩽ 0 and variance. We also reveal a complementary character between the criteria based on the generalized Wigner–Yanase skew information and an alternative one based on variance through specific examples. We illustrate the merits of these criteria and show that the combination of the entanglement criteria has a stronger detection capability, as it is capable of detecting entangled states that remain unrecognized by other criteria.
The kkk-nonseparability is a kind of multipartite quantum correlation which can be used to characterize some aspects of multipartite entanglement. In this paper, we discuss the detection of kkk-nonseparability of nnn-partite quantum states from an information perspective and obtain some kkk-nonseparability criteria in terms of quantum Fisher information. These criteria can identify many kkk-nonseparable states, and their advantages over an important and well-known kkk-nonseparability criterion [M. Huber et al., Phys. Rev. A 88, 042328 (2013)] are illustrated by several typical examples.
A Bell-type inequality is proposed in terms of Wigner-Yanase skew information, which is quadratic and involves only one local spin observable at each site. This inequality presents a hierarchic classification of all states of multipartite quantum systems from separable to fully entangled states, which is more powerful than the one presented by quadratic Bell inequalities from two-entangled to fully entangled states. In particular, it is proved that the inequality provides an exact test to distinguish entangled from nonentangled pure states of two qubits. Our inequality sheds considerable light on relationships between quantum entanglement and information theory.
In order to quantify the information content of quantum states in the presence of conserved quantities, Wigner and Yanase introduced the notion of skew information [Proc. Natl. Acad. Sci. USA 49, 910, (1963)], which was later identified as a paradigmatic version of quantum Fisher information. The skew information is quite different from, yet deeply connected with, the ubiquitous quantum entropies and has important applications in quantum theory. In this paper, pursuing further the original idea of Wigner and Yanase, we propose a measure for correlations in terms of the skew information, investigate its fundamental properties, and elucidate its characteristics. An appealing feature of this measure for correlations is that its evaluation does not involve any optimization, in sharp contrast to the entanglement and discord measures, and can be straightforwardly calculated. In particular, the algorithm and explicit formulas for general bipartite states are prescribed, and simple analytical expressions for some special states, including arbitrary bipartite pure states, the Bell-diagonal states, and some highly symmetric states such as the Werner states and the isotropic states, are obtained.